TY  - BOOK
AU  - Hoeven,Joris
ED  - SpringerLink (Online service)
TI  - Transseries and Real Differential Algebra
T2  - Lecture Notes in Mathematics,
SN  - 9783540355915
AV  - QA564-609 
U1  - 516.35 23
PY  - 2006///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Geometry, algebraic
KW  - Functional equations
KW  - Differentiable dynamical systems
KW  - Algebraic Geometry
KW  - Difference and Functional Equations
KW  - Dynamical Systems and Ergodic Theory
N1  - Orderings -- Grid-based series -- The Newton polygon method -- Transseries -- Operations on transseries -- Grid-based operators -- Linear differential equations -- Algebraic differential equations -- The intermediate value theorem
N2  - Transseries are formal objects constructed from an infinitely large variable x and the reals using infinite summation, exponentiation and logarithm. They are suitable for modeling "strongly monotonic" or "tame" asymptotic solutions to differential equations and find their origin in at least three different areas of mathematics: analysis, model theory and computer algebra. They play a crucial role in Écalle's proof of Dulac's conjecture, which is closely related to Hilbert's 16th problem. The aim of the present book is to give a detailed and self-contained exposition of the theory of transseries, in the hope of making it more accessible to non-specialists
UR  - http://dx.doi.org/10.1007/3-540-35590-1
ER  -